The Mechanics of Bird Migration

Abstract

Summary A theory is presented for calculating the relation between mechanical power required to fly and forward speed, for a bird flying horizontally. The significance of this for migration is explained, and quick methods are given (and summarized in the Appendix) for calculating key points on the curve. Speed ranges and effective lift: drag ratios are calculated for a number of different flying animals. Factors affecting migration range are discussed, and the effects of head‐ and tailwinds are considered. Still‐air range depends on effective lift: drag ratio, but not on size or weight as such. The relation of power required to that available from the muscles is considered. Small birds have a greater margin of power available over power required than large ones, and tend to run their flight muscles at a lower stress, or lower specific shortening, or both. There is an upper limit to the mass of practicable flying birds, represented approximately by the Kori Bustard Ardeotit kori. The effect of adding extra weight (food or fuel) is to increase both minimum‐power speed, and maximum‐range speed, in proportion to the square root of the weight, and to increase the corresponding powers in proportion to the three‐halves power of the weight. Birds up to about 750 g (fat‐free) can double their fat‐free mass, and still have sufficient power to fly at the maximum‐range speed. Larger birds are progressively more severely limited in the maximum loads they can carry, and this reduces their range. Many large birds migrate by thermal soaring, thus economizing on fuel at the expense of making slower progress. During a long flight both speed and power have to be progressively reduced as fuel is used up. A formula is given for calculating the still‐air range of a bird which does this in an optimal fashion. The only data required are the effective lift: drag ratio, and the proportion of the take‐off mass devoted to fuel. Increase of height has no effect on the still‐air range, but the optimum cruising speed (and power) is increased. The optimum cruising height is reached when the bird can absorb oxygen just fast enough to maintain the required power. The optimum height increases progressively as fuel is used up. No range is lost as a result of the work done in climbing to the cruising height.

Behavioural mapping of a pelagic seabird: combining multiple sensors and a hidden Markov model reveals the distribution of at-sea behaviour

“…Assuming that the movement speeds calculated here from the GPS (which include wind velocity) are reasonably representative of flight speeds (which exclude wind velocity), this is within the theoretical flight speed range previously calculated for Manx shearwaters [32], but slightly slower than that calculated from previous GPS tracking (11 m s 21 ), using devices of similar mass [2]. For long-distance movements, birds may be expected to fly close to their maximum range velocity (ca 14 m s 21 ; [32]). Here, it seems that birds were flying closer to their minimum power velocity (ca 7.5 m s 21 ; [32]), suggesting some exploitation of non-powered flight such as shear-soaring [34].…”

“…First, it was characterized by high-speed movement (median speed ¼ 8.9 m s 21 ), within the theoretical flight speed range for the species [32]. Second, there was high or constant contact with the sea surface (median proportion of time immersed ¼ 0).…”

“…For long-distance movements, birds may be expected to fly close to their maximum range velocity (ca 14 m s 21 ; [32]). Here, it seems that birds were flying closer to their minimum power velocity (ca 7.5 m s 21 ; [32]), suggesting some exploitation of non-powered flight such as shear-soaring [34]. Flight activity typically persisted over long periods and occurred where birds travelled long distances, often via relatively direct routes (figure 4).…”

Migration by soaring or flapping: numerical atmospheric simulations reveal that turbulence kinetic energy dictates bee-eater flight mode

“…Nonetheless, for large bird species, overall progress by flapping averaged over the entire journey (including stopovers) is slower than that of soaring-gliding. This is because the metabolic demands of flapping flight increase disproportionately with body mass [10,12], and large flapping species must consequently obtain large fuel stores that their deposition necessitates lengthy stopover periods. The soaring-gliding flight mode is unfavourable to small migrating birds because gliding speed, and hence the speed of progression, declines with body mass [11].…”

“…Migrating birds are known to use two principal modes of flight when traversing land areas. During powered flapping flight, progress is made through continuous self-propulsion by the bird's wings [10], while during soaringgliding, the wings are held in an outstretched position, and progress is obtained by exploiting energy available in the environment [11]. Soaring -gliding flight comprises two alternating phases, ascent soaring, usually achieved by circling in convective updraughts during which the bird gains potential energy, and descent gliding, during which the bird uses its potential energy to move forward by sinking in the air.…”